Exponentials & Logarithms Flashcards

Exponentials & Logarithms Flashcards
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Solve the equation for x: 3x = 81
x = 4
Got it
Evaluate the logarithm: log4 (64)

log4 (64) = 3

Got it
Evaluate the logarithm: log2 (32)

log2 (32) = 5

Got it
Evaluate the logarithm: log5 (25)

log5 (25) = 2

Got it
Evaluate the logarithm: log3 (81)

log3 (81) = 4

Got it
State the base of this logarithm: log7 (49)

The base is 7.

Got it
State the base of this logarithmic expression: log(7)
A log without a given base always has a base of 10.
Got it
Exponential Growth
A quantity that increases with time in a manner that can be represented by the function y = ACt. A represents the initial amount at time t = 0 and C is a constant for the specific situation.
Got it
Rewrite the equation so that it is solved for x: 7 = e(x - 3)
x = ln(7) + 3
Got it
Evaluate the expression: log(0.001)
log(0.001) = -3
Got it
Rewrite the logarithmic expression in simpler form: 3log(x) - log(y)
The simplified form is log(x3/y)
Got it
Rewrite the equation so that it is solved for t: 10(t - 7) = 3
t = log(3) + 7
Got it
Rewrite the equation so that it is solved for n: 10(n + 2) = 534
n = log(534) - 2
Got it

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Flashcard Content Overview

How do you solve an equation that has a variable as an exponent? This set of flashcards will give you some practice problems on concepts related to exponential equations and logarithms. This includes rewriting logarithms using their properties, as well as the relationship between logarithms and exponents. You can also review a few exponential growth and decay problems.

Front
Back
Rewrite the equation so that it is solved for n: 10(n + 2) = 534
n = log(534) - 2
Rewrite the equation so that it is solved for t: 10(t - 7) = 3
t = log(3) + 7
Rewrite the logarithmic expression in simpler form: 3log(x) - log(y)
The simplified form is log(x3/y)
Evaluate the expression: log(0.001)
log(0.001) = -3
Rewrite the equation so that it is solved for x: 7 = e(x - 3)
x = ln(7) + 3
Exponential Growth
A quantity that increases with time in a manner that can be represented by the function y = ACt. A represents the initial amount at time t = 0 and C is a constant for the specific situation.
State the base of this logarithmic expression: log(7)
A log without a given base always has a base of 10.
State the base of this logarithm: log7 (49)

The base is 7.

Evaluate the logarithm: log3 (81)

log3 (81) = 4

Evaluate the logarithm: log5 (25)

log5 (25) = 2

Evaluate the logarithm: log2 (32)

log2 (32) = 5

Evaluate the logarithm: log4 (64)

log4 (64) = 3

Solve the equation for x: 3x = 81
x = 4
Solve the equation for x: 125 = 5x
x = 3
Solve the equation for n: 6n = 1296
x = 4
Evaluate the equation: 5n = 20
The value of n is approximately 1.86.
Evaluate the equation: 3t = 27
t = 3
Evaluate the expression: log3 (1)
log3 (1) = 0
Write the exponential function that represents the balance in a bank account after t years if your initial deposit is \$2000 and the interest rate is 3%.
2000(1.03)t
Write the exponential function that represents the value of a motorcycle after 3 years if you bought it for \$12,000 and it depreciates at a rate of 12% per year.
12000(0.88)3
Find the yearly rate of depreciation for the following situation. A used motorcycle was purchased for \$8000. Five years later, its value has depreciated to \$2621.
The rate of depreciation was approximately 20% per year.
Rewrite the logarithmic expression in simplest form: log(x3) + 2log(x) - 3log(y)
The simplified form is log(x5/y3).
Rewrite the logarithmic expression in simplest form: 2ln(e 2) + 3 lnx
The simplified form is 4 + ln(x3).
Give another way to write the expression: ln(x4)
ln(x4) can also be written as 4ln(x).
Evaluate the equation: ln(3) + ln(x) = 5
x = e5/3
Evaluate the equation: 3ln(x) + ln(5) = 2ln(x) + 6
x = e6/5
Give another way to write the expression: 3 + 2ln(e4) - 3ln(t)
11 + ln(1/t3)

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